Best Known (177, 177+59, s)-Nets in Base 4
(177, 177+59, 1028)-Net over F4 — Constructive and digital
Digital (177, 236, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 59, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(177, 177+59, 2137)-Net over F4 — Digital
Digital (177, 236, 2137)-net over F4, using
(177, 177+59, 294257)-Net in Base 4 — Upper bound on s
There is no (177, 236, 294258)-net in base 4, because
- 1 times m-reduction [i] would yield (177, 235, 294258)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3048 670852 132341 480978 064783 034428 427816 762167 450804 586248 297062 662669 894565 544450 312812 908504 126997 050038 701362 092664 521738 899352 371645 614344 > 4235 [i]